They turn green, from any chemicals stored under the sink, not just because. I have Copper under my bath & Kitchen sink, never have had any issues with it turning Green. If it does, it will do it at the joints, before the whole section.

Wipe your fittings with soap and water to remove the flux residue.
You can paint them if you want.....

Ayuh,.... When I redid the bathroom in my rental, 'bout 8 years ago, the shower pipes were gonna be "Exposed", so I cleaned 'em up with a green scotch pad, 'n painted 'em with clear Rustoleum enamel,...

As for keeping copper shiny, I have a copper mailbox that I put what amounts to musical instrument grade clear coat on it (I have a can left, but it's packed away otherwise I'd mention the name). I applied six coats. Six years later, even after being out in full sun and the elements (south-facing, no shade) it still looks brand new. I'll probably put on a fresh coat or two before reinstalling it at the new house. So it "can" be done, but for under a sink? Why bother?

I guess I wouldn't spend too much time seeing that they're going to be underneath / inside a cabinet. No matter what with copper it will eventually dull the look. But yes after soldering wipe Fittings with wet rag to clean the excess flux off.